arXiv 0801.34522008-01-22math.GRmath-phmath.MPnlin.SI

Harish-Chandra integrals as nilpotent integrals

M. Bertola, A. Prats Ferrer

备注：: 10 pages

英文摘要：

Recently the correlation functions of the so-called Itzykson-Zuber/Harish-Chandra integrals were computed (by one of the authors and collaborators) for all classical groups using an integration formula that relates integrals over compact groups with respect to the Haar measure and Gaussian integrals over a maximal nilpotent Lie subalgebra of their complexification. Since the integration formula a posteriori had the same form for the classical series, a conjecture was formulated that such a formula should hold for arbitrary semisimple Lie groups. We prove this conjecture using an abstract Lie-theoretic approach.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Harish-Chandra highest weight representations of semisimple Lie algebras and Lie groups

In this expository paper we describe the theory of Harish-Chandra highest weight representations and their explicit geometric realizations.

2022-08-30math.GRmath.RT

Harish-Chandra--Schwartz's algebras associated with discrete subgroups of Semisimple Lie groups

We prove that the Harish-Chandra--Schwartz space associated with a discrete subgroup of a semisimple Lie group is a dense subalgebra of the reduced $C^*$-algebra of the discrete subgroup. Then, we prove that for the reduced $C^*$-norm is controlled by the norm of the Harish-Chandra--Schwartz space. This inequality is weaker than property RD and holds for any discrete group acting isometrically, properly on a Riemannian symmetric space.

2016-07-26math.GRmath.OAmath.RT

Bounding Harish-Chandra series

We use the progenerator constructed in our previous paper to give a necessary condition for a simple module of a finite reductive group to be cuspidal, or more generally to obtain information on which Harish-Chandra series it can lie in. As a first application we show the irreducibility of the smallest unipotent character in any Harish-Chandra series. Secondly, we determine a unitriangular approximation to part of the unipotent decomposition matrix of finite orthogonal groups and prove a gap result on certain Brauer character degrees.

2017-01-05math.GRmath.RT

Generalization of Harish-Chandra's basic theorem for Riemannian symmetric spaces of non-compact type

A basic exact sequence by Harish-Chandra related to the invariant differential operators on a Riemannian symmetric space G/K is generalized for each K-type in a certain class which we call `single-petaled'. The argument also includes a further generalization of Broer's generalization of the Chevalley restriction theorem.

2005-02-11math.GRmath.RT

Harish-Chandra pairs in the Verlinde category in positive characteristic

In this article, we prove that the category of affine group schemes of finite type in the Verlinde category is equivalent to the category of Harish-Chandra pairs in the Verlinde category. Subsequently, we extend this equivalence to an equivalence between corresponding representation categories and then study some consequences of this equivalence to the representation theory of $GL(L)$, with $L$ a simple object in the Verlinde category.

2022-03-07math.AGmath.GRmath.RA

Inductive local-global conditions and generalized Harish-Chandra theory

We work towards a version of generalized Harish-Chandra theory compatible with Clifford theory and with the action of automorphisms on irreducible characters. This provides a fundamental tool to verify the inductive conditions for the so-called local-global conjectures in representation theory of finite groups in the crucial case of groups of Lie type in non-defining characteristic. In particular, as shown by the author in an earier paper, this as a strong impact on the verification of the inductive condition for Dade's Conjecture. As a by-product, we also show how to extend the parametrizatio…

2022-05-16math.GRmath.RT

更多相关论文收起更多论文

Small spherical nilpotent orbits and K-types of Harish Chandra modules

Let G be a connected linear semisimple Lie group with Lie algebra g and maximal compact subgroup K. Let K_C -> Aut(p_C) be the complexified isotropy representation at the identity coset of the corresponding symmetric space. Suppose that O is a nilpotent K_C-orbit in p_C, and bar(O} is its Zariski closure in p_C. We study the K-type decomposition of the ring of regular functions on bar(O} when O is spherical and ``small''. We also show that this decomposition gives the asymptotic directions of K-types in any irreducible (g_C, K)-module whose associated variety is bar(O).

2006-12-31math.GRmath.RT

Harish-Chandra 对的多种实例

Various instances of Harish-Chandra pairs

本文将 Harish-Chandra 对技术从 N-分次李代数积分推广到 Z-分次情形，并进一步扩展到代数胚框架，以作用李代数胚为主要例子。

2022-07-14math.DGmath.GRmath.RA

Galois Automorphisms on Harish-Chandra Series and Navarro's Self-Normalizing Sylow $2$-Subgroup Conjecture

G. Navarro has conjectured a necessary and sufficient condition for a finite group $G$ to have a self-normalizing Sylow 2-subgroup, which is given in terms of the ordinary irreducible characters of $G$. In a previous article, the author has reduced the proof of this conjecture to showing that certain related statements hold for simple groups. In this article, we describe the action of Galois automorphisms on the Howlett-Lehrer parametrization of Harish-Chandra induced characters. We use this to complete the proof of the conjecture by showing that the remaining simple groups satisfy the require…

2018-04-09math.GRmath.RT

哈里-恰特拉奇在$\mathbb Z_2 \times \mathbb Z_2$分级世界中的冒险

Integration à la Harish-Chandra for Bi-Graded Lie Algebras

LaSIE UMR 7356 CNRS / La Rochelle University（拉罗谢尔大学）

本文研究了$\mathbb Z_2 \times \mathbb Z_2$双分级李代数的性质，并探讨了基于哈里-恰特拉奇对的李群-代数对应关系及其应用。

2026-09-28math.AGmath.DGmath.GR